The visa they apply for is defined and generally treated by the following:
INA 101 (a)
(15) The term ``immigrant'' means every alien except an alien who is
within one of the following classes of nonimmigrant aliens--
(B) an alien (other than one coming for the purpose of study or
of performing skilled or unskilled labor or as a representative of
foreign press, radio, film, or other foreign information media
coming to engage in such vocation) having a residence in a foreign
country which he has no intention of abandoning and who is visiting
the United States temporarily for business or temporarily for
pleasure;
8 CFR 214.2
(b) Visitors —(1) General. Any B–1 visitor for business or B–2 visitor for pleasure may be admitted for not more than one year and may be granted extensions of temporary stay in increments of not more than six months each, except that alien members of a religious denomination coming temporarily and solely to do missionary work in behalf of a religious denomination may be granted extensions of not more than one year each, provided that such work does not involve the selling of articles or the solicitation or acceptance of donations. Those B–1 and B–2 visitors admitted pursuant to the waiver provided at §212.1(e) of this chapter may be admitted to and stay on Guam for period not to exceed fifteen days and are not eligible for extensions of stay.
(2) Minimum six month admissions. Any B–2 visitor who is found otherwise admissible and is issued a Form I–94, will be admitted for a minimum period of six months, regardless of whether less time is requested, provided, that any required passport is valid as specified in section 212(a)(26) of the Act. Exceptions to the minimum six month admission may be made only in individual cases upon the specific approval of the district director for good cause.
(3) Visa Waiver Pilot Program. Special requirements for admission and maintenance of status for visitors admitted to the United States under the Visa Waiver Pilot Program are set forth in section 217 of the Act and part 217 of this chapter.
etc....
CAUTION: Many U.S. residents (USC's and LPR's) get overly involved in their alien relatives' application for a nonimmigrant B-1/B-2 visa and end up hurting their chances. They start providing TOO MUCH INFORMATION and offering to "sponsor" their alien relatives from the very beginning. This action often defeats their alien relatives' efforts to show their strong ties to their home country, their financial stability that allows them to make a temporary pleasure trip, and their intent not to abandon their foreign residence. In short, they sucker-punch their alien relatives statements as to a lack of "immigrant intent".
On the other hand, less aggressive statements of support can be quite helpful, if handled right:
1.) Invitations to visit for specific events, birthdays, graduations, anniversaries, weddings or holidays (secular/national, social/cultural, or religious) can go either way. Some events have ambiguous consequences. Ask yourself if that particular event could be seen as making a major change in circumstances. Does the event place the U.S. resident in a position to immediately petition and sponsor the visitor for adjustment of status? Mom and Dad coming specifically for a Naturalization Ceremony is bad but for an Aunt and Uncle it is irrelevant, for a sibling, it would take a decade to result in an immigrant visa, therefore, should be seen as irrelevant.
2.) Offers of accommodation can be helpful by reducing the alien relatives financial burden. "Mom, when you come to visit, the kids will double-up and you and dad can have Hakeem's room." would be better than "Mom, as promised, the in-law apartment is ready for you and dad to move in".
3.) Definite (or even vague) plans and itineraries help. Mentioning the sites to be visited and activities available during the planned visit supports the tourist visit purpose of the B-2 entry. Many communities have ethnic celebrations: San Francisco makes a big deal out of Chinese New Year while Milwaukee has a huge Oktoberfest and Buffalo, NY has a first rate Hellenic Festival (Greek Orthodox), New York City has Broadway, the Statue of Liberty etc.., for example.
4.) As a last resort, an offer to submit an I-134, Affidavit of Support, can be the make or break decision. Will it cement eligibility for relatives of limited means OR will it blow away claims of nonimmigrant intent???? It's a situational decision that can go either way.
Best of luck,